This is because you are using NTLM authentication and Windows authentication between the servers.
NTLM only allows you to connect to one server, and does not allow that server to forward your authentication along to the third server.
Your options to fix this are:
1. Enable Kerberos authentication for the servers (check with your network admin on how to get this setup).
2. Setup the linked servers to log into the remote SQL servers using SQL Authentication instead of Windows Authentiction.
This error will come up regardless of OS or SQL Server version.